Fourteen-man Clare took full advantage of Down's profligacy in front of goals to secure a valuable away win in Division Two of the Allianz Football League.
Although they were never ahead in the game, Down controlled it for long spells but hit 15 wides on a frustrating afternoon in Páirc Esler as their poor home league form continued.
Clare scored just three points in the second half, having led 1-09 to 1-05 at the interval, and had defender Ciaran Russell sent-off after 54 minutes for a black card offence.
He was dismissed having already been booked in the incident which led to a Down penalty three minutes into the second half but in another sign of Down's wastefulness, Darragh O'Hanlon blazed the penalty over the bar.
It's a result which eases Clare's relegation worries a little, but they are still vulnerable – as are Down, who are also sitting on four points after four games.
Having lost seven out of eight home league games in the last three seasons, they might not be too disappointed two of their last three games in this campaign are away.
Sean O'Donoghue's goal after 35 seconds was the perfect start for Clare, the forward cutting through the right side of Down's defence and blasting the ball high into the roof of the net.
Eoin Cleary quickly added the first of his five first-half frees to put Clare 1-1 to no score ahead, but Down responded well and hit four unanswered points to draw level by the ninth minute.
Donal O'Hare scored three of them, two from frees, with Shay Millar landing the equaliser.
Cleary was outstanding from placed balls and his left-footed sideline conversion from inside the 21-yard line was the most memorable score of the day.
The unmarked O'Hare tapped into an open net after Caolan Mooney did all the hard work, his searing pace and unselfish fisted pass across goal teeing him up for a simple finish after 19 minutes.
That left it 1-04 apiece but it was the last time they were level with Clare hitting five of the next six points before half time, Keelan Sexton, Kieran Malone and four Cleary frees stretching them four clear at the break.
Russell's high tackle on David McKibbin gave Down a penalty and a way back into the game, but O'Hanlon's kick sailed high over the bar.
The second half became a little niggly as tempers boiled over on a few occasions and the closest Down got was to within two points, despite the best efforts of Mooney and Aaron Morgan who landed points.
O'Hare missed three frees, another sign of Down's wastefulness, while in contrast Clare only had two wides in the entire game and only one of those was actually a shooting attempt.
Down 'won' the second half by five points to three, but Clare hung on for their first league win of the season.
Down: M Reid; C Flanagan, B McArdle, A Doherty (0-02); D O'Hagan, N McParland, C Mooney (0-01); D McKibbin, N Donnelly; D O'Hanlon (0-01), C Maginn, S Millar (0-01); B O'Hagan, D O'Hare (1-04), R Johnston
Subs: K McKernan for McKibbin (BC, 51), A Morgan (0-01) for R Johnston (51), C Poland for Maginn (51), R Wells for O'Hanlon (63), S Dornan for B O'Hagan (69)
Clare: K Roche; C O'Dea (0-01), C Brennan, E Collins (0-01); C Russell, A Fitzgerald, P Lillis; G Brennan, C O'Connor; K Malone (0-01), E Cleary (0-07), G O'Brien; S O'Donoghue (1-00), K Sexton (0-01), D Tubridy (0-01)
Subs: A Sweeney for O'Brien (46), C Finucane for Sweeney (68), D Bohannon for Malone (70), E Courtney for Sexton (70)
Referee: James Molloy (Galway)